defined for all \(x\in \mathop {\bf dom}(f+h)\)  and \(z\in \mathop {\bf dom}g^*\) .
This follows from the fact that the functions \(f+h+\delta _X\)  and
\(g^*+\delta _Z\)  are closed and co-finite, so their conjugates
have full domain [1]}.
If \(\eta (x,z)\)  is easily computed, and \(\eta (x,z) \ge 0\)  for all
\(x\in \mathop {\bf dom}(f+h)\)  and \(z\in \mathop {\bf dom}g^*\)  with equality only if
\(x\)  and \(z\)  are optimal, then the function \(\eta \) 
can serve as a merit function in primal–dual algorithms
for problem (REF ).
